Refer to Exercises 31 and 33. The relationship between median torques and median speeds is called the relationship between soils. The relationships between torque and speed restricted to a certain soil are called the relationships within soils. Is the relationship within soils the same as the relationship between soils, or is it the opposite? Explain.

Data From Exercise 31:

Which statement best describes the results of Exercise 30?
i. For soils where the median torque is greater, the median speed is greater.
ii. For soils where the median torque is greater, the median speed is less.

Data From Exercise 30:

For each of the following types of soil, find the median torque and median speed for all observations in that soil.
a. GSG soil
b. CCS soil
c. GSF soil
d. GSGu soil

Data From Exercise 33:

Which statement best describes the results of Exercise 32?
i. For each of the four soils, we are \(95 \%\) confident that the mean speed is greater when the torque is lower.
ii. For each of the four soils, we are \(95 \%\) confident that the mean speed is greater when the torque is greater.

Data From Exercise 32:

For each of the following types of soil, find the median value of the torque for all observations in that soil. Then let \(\mu_{L}\) be the mean speed when the torque is below the median, let \(\mu_{U}\) be the mean speed when the torque is above the median, and find a \(95 \%\) confidence interval for \(\mu_{U}-\mu_{L}\).
a. GSG soil
b. CCS soil
c. GSF soil
d. GSGu soil